On the stability of Appolonius' equation
Jun, Kil-Woung ; Kim, Hark-Mahn
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, p. 615-624 / Harvested from Project Euclid
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In this paper, using an idea from the direct method of Hyers and Ulam, we investigate the situations so that the generalized Hyers-Ulam stability problem for Appolonius' equation \begin{eqnarray} \nonumber f(x-z)+f(y-z)={1 \over 2}f(x-y)+2f\Big(z-{x+y \over 2}\Big) \end{eqnarray} is satisfied.
Publié le : 2004-12-14
Classification:  Hyers-Ulam stability,  quadratic function,  Appolonius' equation,  39A11,  39B72 
@article{1102689125,
     author = {Jun, Kil-Woung and Kim, Hark-Mahn},
     title = {On the stability of Appolonius' equation},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {1},
     year = {2004},
     pages = { 615-624},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1102689125}
}

Jun, Kil-Woung; Kim, Hark-Mahn. On the stability of Appolonius' equation. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp.  615-624. http://gdmltest.u-ga.fr/item/1102689125/